On Friday, prime minister Theresa May set out her plans to reform the UK's education system, including proposals to remove the ban on creating new grammar schools.

May said her controversial plans to increase selection in state schools would attempt to address inequality in the education system that sees talented children from low-income families achieving on average markedly lower grades than their richer counterparts.

Most of the figures concern England, as education policy in Scotland, Wales, and Northern Ireland is devolved – though Northern Ireland in particular retains a large number of grammar schools.

Grammar schools select most or all of their pupils by ability.

It's the entrance test that differentiates grammars from the majority of state schools. While other schools can select based on religious faith, or can select a small minority (up to 10%) based on ability in a specific subject, grammar schools set an entrance exam – usually referred to as the "11+" – and admit the pupils with the highest scores.

These exams are often highly competitive, with typical ratios between 1 in 3 and 1 in 8 of school places per test taker.

You can take a look at a sample English 11+ paper here, or a sample Maths paper here.

Many parents pay for tuition to prepare their kids for the 11+.

Part of the controversy around grammar schools centres around the idea that middle-class families benefit much more from the system than working-class ones. Part of this is reinforced by many middle-class parents arranging after-school tuition to help their children pass the 11+ exam.

A 2009 report found the average cost of this tuition was around £24 an hour – well beyond the UK's average hourly wage – reaching up in some cases to £60. With a typical student preparing for the 11+ taking around 20 hours of tuition, this is a serious cost for a typical family – though well below the cost of a private school.

Grammar schools never really went away.

Research by the House of Commons library found there are currently 167,000 pupils in grammar schools – around 1 in 20 of total school places. At their peak, around 1 in 5 school places were at grammars.

The number of grammar school places is actually an increase versus 1997, when New Labour entered power, suggesting that the UK's remaining grammar schools have quietly expanded in recent decades, despite the ban on opening new schools.

Grammar schools are really good schools.

This research from the Sutton Trust is a little old – it's from 2005 – but shows how high the performance of grammar schools is. Of the UK's top 200 state schools, 161 are grammar schools – meaning that all but two of the UK's grammar schools are in the overall top 200.

It is important to note that this is in large part a function of the students who go to grammar schools: If a school gets to slice off the most able students in its area, it will almost certainly get good results by default.

Many grammar schools also score well on "value added", a measure which takes into account the ability of students, but again, grammars benefit from having to cater to a much narrower range of abilities than most state schools.

Grammar schools don't take many poorer students, though.

The UK's remaining grammar schools are quite concentrated in a few local authorities, and these areas are already richer than the UK as a whole. Even taking that into account, though, grammar school pupils tend to come from wealthier families than other schools in the area – suggesting fears that grammars sustain inequality may be well-founded.

Research by the Sutton Trust found 11.7% of students living in areas with grammar schools receive free school meals – a measure of pupils from low-income families – but only 2.1% of students attending those grammars are on free school meals, meaning that grammars' intake of students is not representative of their local areas.

Grammar schools don't help the overall achievement of the areas they're in.

This is the real crunch issue for grammar schools: Virtually no one disputes that grammar schools are good for those pupils lucky enough to get in, but the evidence suggests they don't improve the overall results of students in the area.

Given that grammars perform well, this means that students who live in areas with grammar schools but don't attend one do markedly worse than equivalent students elsewhere.

Chris Cook, now policy editor at BBC Newsnight, did an extensive analysis using the National Pupil Database for the Financial Times comparing areas with grammar schools – dubbed "selectavia" – to other regions.

His results showed that counties with grammar schools performed about middle-of-the-pack – London's schools (which are overwhelmingly comprehensive) are the best by a significant margin. The FT analysis also showed selective counties were middling for students on free school meals, scotching claims grammars are particularly good for social mobility.

Most striking, though, is this chart (reproduced with permission from Cook):

The chart compares areas with grammar schools (the black line) to everywhere else (the pink line), and compares richer and poorer families. The left-hand side of the chart shows poorer pupils in counties with grammars getting noticeably worse results than their counterparts.

The far-right-hand side of the chart, in contrast, shows a benefit to a small fraction of children from the very richest families. In short, grammars appear to benefit a small number of children of rich parents at the expense of a larger number of children of poorer ones.

May has said she will take steps to ensure new grammars are accessible to pupils from all backgrounds. The evidence so far is clear that existing ones have not, on average, achieved this goal.

James Ball is a special correspondent for BuzzFeed News and is based in London.
PGP: here